Bifurcation Control and Universal Unfolding for Hopf-Zero Singularities with Leading Solenoidal Terms

DOI10.1137/141000403zbMath1352.34053arXiv1412.5399OpenAlexW3098446760MaRDI QIDQ2808179

Majid Gazor, Nasrin Sadri

Publication date: 20 May 2016

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.5399

zbMATH Keywords

solenoidal vector fieldsbifurcation controlHopf-zero singularityprimary and secondary bifurcationsuniversal asymptotic unfolding

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Bifurcation control of ordinary differential equations (34H20)

Related Items (12)

Stability and bifurcation in a two-patch model with additive Allee effect ⋮ Tone colour in music and bifurcation control ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ Hopf-zero bifurcation of oregonator oscillator with delay ⋮ Normal Form Analysis of ℤ2-Equivariant Singularities ⋮ Vector potential normal form classification for completely integrable solenoidal nilpotent singularities ⋮ Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system ⋮ Bifurcation control and sound intensities in musical art ⋮ High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities ⋮ Bifurcation Controller Designs for the Generalized Cusp Plants of Bogdanov--Takens Singularity with an Application to Ship Control ⋮ Leaf-normal form classification for \(n\)-Tuple Hopf singularities

Uses Software

• Maple
• Singularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• About the unfolding of a Hopf-zero singularity
• Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case
• Unique normal forms for planar vector fields
• Spectral sequences and parametric normal forms
• Linear grading function and further reduction of normal forms
• Hypernormal form theory: foundations and algorithms
• Unique normal forms: The nilpotent Hamiltonian case
• Box products in nilpotent normal form theory: the factoring method
• An improved theory of asymptotic unfoldings
• Singularities and groups in bifurcation theory. Volume I
• Further reduction of the Takens-Bogdanov normal form
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Asymptotic unfoldings of dynamical systems by normalizing beyond the normal form
• Normal form theory and spectral sequences.
• Bifurcation control. Theory and applications
• Singularities of vector fields
• Normal forms for Hopf-zero singularities with nonconservative nonlinear part
• Unique normal form of a class of 3 dimensional vector fields with symmetries
• Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity
• Unique orbital normal forms for vector fields of Hopf-zero singularity
• Volume-preserving normal forms of Hopf-zero singularity
• FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS
• Periodic and Steady-State Mode Interactions Lead to Tori
• Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
• THE CUSP–HOPF BIFURCATION
• Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems
• Singularities of vector fields on
• Bifurcation and Normal Form of Nonlinear Control Systems, Part I
• Bifurcation and Normal Form of Nonlinear Control Systems, Part II
• Analysis and Control of Hopf Bifurcations
• Normal Forms and Unfoldings for Local Dynamical Systems
• The simplest normal form of Hopf bifurcation
• Hypernormal Form for the Hopf-Zero Bifurcation
• Normal forms of Hopf-zero singularity
• Controllability and local accessibility - A normal form approach
• BIFURCATION CONTROL: THEORIES, METHODS, AND APPLICATIONS
• Elements of applied bifurcation theory

This page was built for publication: Bifurcation Control and Universal Unfolding for Hopf-Zero Singularities with Leading Solenoidal Terms